| Title:
|
Finite groups whose all proper subgroups are $\mathcal {C}$-groups (English) |
| Author:
|
Guo, Pengfei |
| Author:
|
Liu, Jianjun |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
513-522 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A group $G$ is said to be a $\mathcal {C}$-group if for every divisor $d$ of the order of $G$, there exists a subgroup $H$ of $G$ of order $d$ such that $H$ is normal or abnormal in $G$. We give a complete classification of those groups which are not $\mathcal {C}$-groups but all of whose proper subgroups are $\mathcal {C}$-groups. (English) |
| Keyword:
|
normal subgroup |
| Keyword:
|
abnormal subgroup |
| Keyword:
|
minimal non-$\mathcal {C}$-group |
| MSC:
|
20D10 |
| MSC:
|
20E34 |
| idZBL:
|
Zbl 06890387 |
| idMR:
|
MR3819188 |
| DOI:
|
10.21136/CMJ.2017.0542-16 |
| . |
| Date available:
|
2018-06-11T10:56:54Z |
| Last updated:
|
2020-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147233 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
